In this note, we study the expander decomposition problem in a more general setting where the input graph has positively weighted edges and nonnegative demands on its vertices. We show how to extend the techniques of Chuzhoy et al. (FOCS 2020) to this wider setting, obtaining a deterministic algorithm for the problem in almost-linear time.
翻译:在本说明中,我们在一个更普遍的环境下研究扩张器分解问题,输入图对它的脊椎具有积极的加权边和无负要求。我们展示了如何将Chuzhoy等人的技术(FOCS 2020)推广到这一更广泛的环境中,在几乎线性时间里为问题获得确定性算法。